Feature Importance for Clustering

The literature on cluster analysis methods evaluating the contribution of features to the emergence of the cluster structure for a given clustering partition is sparse. Despite advances in explainable supervised methods, explaining the outcomes of unsupervised algorithms is a less explored area. This paper proposes two post-hoc algorithms to determine feature importance for prototype-based clustering methods. The first approach assumes that the variation in the distance among cluster prototypes after marginalizing a feature can be used as a proxy for feature importance. The second approach, inspired by cooperative game theory, determines the contribution of each feature to the cluster structure by analyzing all possible feature coalitions. Multiple experiments using real-world datasets confirm the effectiveness of the proposed methods for both hard and fuzzy clustering settings.